Super-rapid three-dimensional topography measurement method and system based on improved fourier transform contour technique

ABSTRACT

A super-rapid three-dimensional measurement method and system based on an improved Fourier transform contour technique is disclosed. The method comprises: firstly calibrating a measurement system to obtain calibration parameters, then cyclically projecting 2n patterns into a measured scene using a projector, wherein n patterns are binary sinusoidal fringes with different high frequency, and the other n patterns are all-white images with the values of 1, and projecting the all-white images between every two binary high-frequency sinusoidal fringes, and synchronously acquiring images using a camera; and then performing phase unwrapping on wrapped phases to obtain initial absolute phases, and correcting the initial absolute phases, and finally reconstructing a three-dimensional topography of the measured scene by exploiting the corrected absolute phases and the calibration parameters to obtain 3D spatial coordinates of the measured scene in a world coordinate system, thereby accomplishing three-dimensional topography measurement of an object. In this way, the precision of three-dimensional topography measurement is ensured, and the speed of three-dimensional topography measurement is improved.

FIELD OF THE INVENTION

The invention belongs to the field of three-dimensional imaging technology, in particular to a super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique.

BACKGROUND OF THE INVENTION

In the past few decades, benefited from the rapid development of electronic imaging sensors, optoelectronic technology and computer vision, 3D image acquisition technology has become more and more mature. However, in areas such as biomechanical analysis, industrial testing, solid mechanics deformation analysis, and vehicle impact testing, it is desirable to be able to obtain three-dimensional topographical information during transient change of an object and then play it back at a slower speed for observation and analysis. Fringe projection contour technique is a widely used method to obtain three-dimensional topographical information of objects, which has the advantages of non-contact, high resolution and strong practicability. Fringe projection contour technique is generally divided into two categories: Fourier transform contour technique and phase-shifting contour technique. Fourier transform contour technique (Fan Yujia's master thesis: the three-dimensional topography of objects using Fourier transform contour technique, 2011) only needs one fringe to obtain the three-dimensional information of an object and the measurement speed is fast, but due to the existence of spectrum overlapping and other problems, the measurement accuracy is lower than that of phase-shifting coutour technique. Although phase-shifting contour technique has high precision, at least three fringe patterns are required to obtain the three-dimensional information of an object, thus limiting its measurement speed. The measurement speed of the currently implemented three-dimensional topography measurement technology cannot meet the needs of a super-rapid three-dimensional topography measurement field.

At the same time, for the hardware technical indicators required for the super-rapid three-dimensional measurement of the fringe projection contour technique, on the one hand, the existing high-speed camera can achieve the speed of 10,000 frames per second for the acquisition of two-dimensional images. The acquisition speed can be faster by reducing the resolution of the captured image. On the other hand, the digital micro-mirror device (DMD) is the main component of a projector, and the rate at which the binary pattern is projected by the optical switch can also reach 10000 Hz. Therefore, hardware is no longer a limiting factor in the measurement speed of fringe projection contour technique. How to reduce the number of fringe images required while ensuring measurement precision is the key to solving the problem. Although traditional Fourier transform contour technique only needs one fringe and has fast measurement speed, once a measured object has the problems like sharp edges, surface discontinuities and surface reflectance changes, the spectrum overlapping will be caused, which will lead to low measurement precision. Researchers have proposed the π phase-shifting Fourier transform contour technique (Guo L. Su X, Li J. “Improved Fourier transform contour technique for the automatic measurement of 3D object shapes”. Optical Engineering, 1990, 29(12): 1439-1444.) and Fourier transform contour technique technique of subtracting background (Guo H, Huang P. “3D shape measurement by use of a modified Fourier transform method”. Proc. SPIE.2008,7066:70660E.), but the former included height information in two sinusoidal fringe patterns, resulting in increased sensitivity to motion, which does not suit to high-speed three-dimensional measurements. The fringe patterns required for the later cannot be accurately produced under a binary pattern projection mode. Once the binary pattern projection mode cannot be used, the measurement speed will be greatly reduced. At the same time, these two improved methods cannot solve the spectrum overlapping problem caused by the large change of surface reflectivity of the measured object. However, for the phase-shifting contour technique, although the measurement precision is high, a lot of fringe patterns are required, which affects the measurement speed. Some researchers have proposed some improved methods, for example, some people propose to use dual-frequency fringe pattern composites method (Liu K, Wang Y, Lau D L. “Dual-frequency pattern scheme for high-speed 3-D shape measurement” Optics express, 2010, 18(5): 5229-5244.). A method of embedding speckle in a fringe pattern has also been proposed (Zhang Y, Xiong Z, Wu F. “Unambiguous 3D measurement from speckle-embedded fringe”. Applied optics, 2013, 52(32): 7797-7805.). However, the improved methods still limit the measurement speed of three-dimensional topography of an object to less than1000 Hz, which cannot meet requirements for three-dimensional topography measurement of super-rapid speed scenes such as bullet leaving a gun and balloon explosions. It can be seen that there is currently no three-dimensional topography measurement method that can achieve ultra-high speed, that is, tens of thousands of frames per second, while ensuring the measurement precision.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a super-rapid three-dimensional measurement method and system based on an improved Fourier transform contour technique, which can significantly improve measurement speed of three-dimensional topography measurement of an object while ensuring the precision of three-dimensional topography measurement of an object.

A technical solution for achieving the object of the present invention is: a super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique; firstly calibrating a measurement system to obtain calibration parameters, the measurement system being composed of a projector, a camera and a computer, and then cyclically projecting 2n (n≥2) patterns onto a measured scene using a projector, wherein n patterns are different binary high-frequency sinusoidal fringes, and the other n patterns are all-white images with the values of 1, and projecting the all-white images between every two binary high-frequency sinusoidal fringes, and synchronously acquiring images using a camera; then using the background normalized Fourier transform contour technique method to obtain the wrapped phase, using temporal phase unwrapping with projection distance minimization (PDM) method to obtain initial absolute phases, using a reliability guided compensation (RGC) of fringe order error method to correct the initial absolute phase and finally, reconstructing a three-dimensional topography of the measured scene with the corrected absolute phases and the calibration parameters to obtain 3D spacial coordinates of the measured scene in a world coordinate system, thereby accomplishing three-dimensional topography measurement of an object.

Compared with the prior art, the present invention has significant advantages: (1) the background normalized Fourier transform contour technique uses a fringe pattern to contain three-dimensional information of a current-moment motion scene, and uses all-white images to remove zero frequency in the spectrum to eliminate the influence of spectrum overlapping caused by sharp edges, surface discontinuity and large changes in surface reflectivity of the measured object while ensuring the measurement precision. (2)using temporal phase unwrapping with projection distance minimization (PDM) method to unwrap the wrapping phase in the case of a separate object in a measured scene, and high-frequency sinusoidal fringes ensure the precision of the measurement, so that the height information contained in each sinusoidal fringe can be used to ensure the measurement speed. (3)The absolute phase obtained by the temporal phase unwrapping with projection distance minimization (PDM) is further corrected by the reliability guided compensation (RGC) of fringe order error method and some error points that may exist due to the motion influence are also corrected, which further ensures the measurement precision. (4)In the experiment, a three-dimensional topography measurement system is built by using a projector with a binary pattern projection speed a camera with an image acquisition speed of 20000 Hz, and a computer. The reconstruction rate of absolute three-dimensional topography at 10000 frames per second is realized by the method of the invention. In the measurement range of 400 mm×275 mm×400 mm, the depth precision is 80 μm, and the time domain error is less than 75 μm. Not only can three-dimensional topography measurement be realized for the general static and dynamic measurement scenes, but also it can be realized for super-fast scenes like bullet leaving a gun and balloon explosions.

The invention is further described in detail below with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is the flow chart of the measurement method of present invention.

FIG. 2 is the experimental measurement results of a static complex scene, i.e., a plaster image and a hand, of present invention.

FIG. 3 is the experimental result of three-dimensional topography measurement of the scene in which a bullet rebounds from a toy gun and hits a plastic plate.

FIG. 4 is the experimental result of three-dimensional topography measurement of a scene in which a darts fly through a balloon and cause the balloon to explode.

FIG. 5 is the schematic map of the measurement subsystem of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

As in combination with FIG. 1 and FIG. 5, the present invention is based on a super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique, firstly calibrating a measurement system to obtain calibration parameters, the measurement system being composed of a projector, a camera and a computer, and then cyclically projecting 2n (n≥2) patterns onto a measured scene using a projector, wherein n patterns are binary sinusoidal fringes with different high frequency, and the other n patterns are all-white images with the values of 1, and projecting the all-white images between every two binary high-frequency sinusoidal fringes, and synchronously acquiring images using a camera; then using the background normalized Fourier transform contour technique method to obtain the wrapped phase, using temporal phase unwrapping with projection distance minimization (PDM) method to obtain initial absolute phases, using a reliability guided compensation (RGC) of fringe order error method to correct the initial absolute phase, and finally reconstructing a three-dimensional topography of the measured scene with the corrected absolute phases and the calibration parameters to obtain 3D spacial coordinates of the measured scene in a world coordinate system, thereby accomplishing three-dimensional topography measurement of an object. The specific implementation steps of the above method are as follows:

Step one, building a measurement subsystem. The measurement subsystem comprises a projector, a camera and a computer, wherein the computer and the projector and the camera are respectively connected by signal lines, and the projector and the camera are connected by trigger lines. There are no strict requirements for the placement of the projector and the camera, as long as scenes that are projected and captured contain the scene to be measured. The computer is equipped with software for controlling the projector and camera and the software can set the parameters of the projector and camera and control the process of the projection of the projector and image acquisition of the camera. MATLAB is also installed in the computer. After images are captured, the process of processing images is realized by MATLAB codes. Using camera calibration method proposed by Zhengyou Zhang (Z. Zhang. “A flexible new technique for camera calibration. “IEEE Transactions on pattern analysis and machine intelligence. 22(11), 1330-1334 (2000).) and the method proposed by Zhang S for the calibration method of structured light 3D measurement system (Zhang S, Huang P S. “Novel method for structured light system calibration”. Optical Engineering, 2006, 45(8): 083601-083601-8.) to calibrate the camera and the projector to obtain calibration parameters, including the internal and external parameters of the camera and the projector.

Step two, the specific processing process of projecting and acquiring images is as follows: the projector cyclically projecting 2n (n≥2) patterns onto a measured scene using a projector, wherein n patterns are different binary high-frequency sinusoidal fringes, and the other n patterns are all-white images with the values of 1, and projecting the all-white images between every two binary high-frequency sinusoidal fringes, and synchronously acquiring images using a camera. The wavelengths of the n high-frequency sinusoidal fringes emitted by the projector must be different, and the wavelengths are marked as {λ₁, λ₂, . . . , λ_(n)}; two conditions must be satisfied when designing wavelength: {circle around (1)} the wavelength of the sinusoidal fringes is sufficiently small (for example a fringe pattern with at least 50 fringes) and ensures that the phase can be successfully retrieved using conventional Fourier transform contour technique; {circle around (2)} the least common multiple of the set of wavelength is greater than or equal to the resolution of the projector along the sinusoidal intensity value, denoted as W. The horizontal resolution of the projector is W, and the projected fringes are vertical fringes (the fringe intensity varies along the lateral direction of the projector). Then the least common multiple between the wavelengths of the sinusoidal fringes needs to be greater than or equal to W, that is, the following formula is satisfied:

LCM(λ₁, λ₂ , L, λ _(n))≥W   (1)

where LCM represents the least common multiple operation and the generated high-frequency sinusoidal fringes are represented by the following formula in the projector space:

I ^(p)(x ^(p) , y ^(p))=a ^(p) +b ^(p) cos(2πf ₀ ^(p) x ^(p))   (2)

where the superscript p is the initial letter of projector and represents the projector space, and I^(p) represents the intensity of the fringe, (x^(p), y^(p)) is the pixel coordinates of the projector, a^(p) is the average intensity of the sinusoidal fringe, b^(p) is the amplitude of the sinusoidal fringe, and f₀ ^(p) is the frequency of the sinusoidal fringes; the halftone technique (Floyd R W. “An adaptive algorithm for spatial gray-scale”. Proc Soc Inf Disp; 1976.) is then used to convert the high-frequency sinusoidal fringes into binary high-frequency sinusoidal fringes, so that the projection speed of the projector can reach the maximum of the inherent projection speed of the projector, ensuring that the hardware does not affect the measurement speed; as the fringe pattern is a binary pattern, both a^(p) and b^(p) in equation (2) are ½, and equation (2) is written as:

I ₁ ^(p)(x ^(p) , y ^(p))=1/2+1/2 cos(2πf ₀ ^(p) x ^(p))   (3)

where I₁ ^(p) represents the intensity of the first high-frequency sinusoidal fringe pattern, the all-white images projected between every two binary high-frequency sinusoidal fringes mean that the values of all the pixels on the projected image are “1”, that is, all micro-mirrors on the digital micro-mirror device DMD—the core components of the projector—are the “on” state and are represented by the following formula:

I ₂ ^(p)(x ^(p) , y ^(p))=1   (4)

where I₂ ^(p) represents the intensity of the all-white images, (x^(p), y^(p)) represents the pixel coordinates of the projector, and the expression of the remaining high frequency sinusoidal fringes is the same as formula (3), except that the frequency f₀ ^(p) is different according to the different wavelength; 2n images are cyclically projected onto a measured scene using a projector, and the camera synchronously acquires the image according to the trigger signal of the projector.

Step three, the wrapped phase is obtained by using a background normalized Fourier transform contour technique method, and the specific process is as follows: wherein in the background normalized Fourier transform contour technique module, after the acquisition of images captured by a camera, every two images are sequentially processed, that is, a high-frequency sinusoidal fringe and a corresponding all-white image; the process is as follows: the high-frequency sinusoidal fringe image and the all-white image captured by a camera are respectively expressed by the following formulas:

I ₁(x ^(c) , y ^(c))=1/2α(x ^(c) , y ^(c))+1/2α(x ^(c) , y ^(c))cos[2πf ₀ x ^(c)+ϕ(x ^(c) , y ^(c))]  (5)

I ₂(x ^(c) , y ^(c))=α(x ^(c) , y ^(c))   (6)

where the superscript c is the initial letter of “camera” and represents a camera space, I₁ is an image captured by a camera after the high-frequency sinusoidal fringe pattern is projected onto the measured scene, I₂ is an image captured by the camera after the all-white image is projected onto the measured scene, (x^(c), y^(c)) is pixel coordinates of the camera, α(x^(c), y^(c)) is the reflectivity of the measured object, f₀ is the sinusoidal fringe frequency, ϕ(x^(c), y^(c)) is the phase containing the depth information of the object, ½α(x^(c), y^(c)) is the zero-frequency part after Fourier transform and its existence will cause spectrum overlapping problem; by using I₁ and I₂ in equations (5) and (6), the influence of the zero-frequency part and the surface reflectivity α(x^(c), y^(c)) of the object to be measured can be removed before performing Fourier transform, see equation (7):

$\begin{matrix} {{I_{d}\left( {x^{c},y^{c}} \right)} = {\frac{{2I_{1}} - I_{2}}{I_{2} + \gamma} = {\cos \left\lbrack {{2\; \pi \; f_{0}x^{c}} + {\varphi \left( {x^{c},y^{c}} \right)}} \right\rbrack}}} & (7) \end{matrix}$

where γ is a constant (such as 0.01) mainly for the purpose of preventing the occurrence of zero as a divisor; then Fourier transform is carried out on the I_(d) after background normalization, and the filter (such as Hanning window) is used to extract the valid information, and then the Fourier inverse transform is performed on the selected spectrum to obtain the wrapped phase. Therefore, using all-white images to remove the influence of the zero-frequency (½α(x^(c), y^(c))) and the reflectivity (α(x^(c), y^(c)) on the surface of the measured object before Fourier transform effectively solve the problem of spectrum overlapping. Through this procedure, the wrapped phase corresponding to each high-frequency sinusoidal fringe acquired by the camera is obtained and contains the depth information of scenes corresponding to each moment when the camera captures the high-frequency sinusoidal fringe pattern. Step four, the initial absolute phase is obtained by using a temporal phase unwrapping with projection distance minimization (PDM) method, and the specific process is as follows: after obtaining the phase corresponding to the high-frequency sinusoidal fringe image acquired by the camera through step three, since its range is wrapped in (−π, π], the phase is called the wrapped phase as there is ambiguity, so it needs to be unwrapped to get the absolute phase, using the wrapped phases corresponding to a set of high-frequency sinusoidal fringes to unwrap each of wrapped phases. The high-frequency sinusoidal fringes projected by a projector in step two are different in wavelength and are recorded as a wavelength vector λ=[λ₁, λ₂, L, λ_(n)]^(T), the wrapped phase vector corresponding to each high-frequency sinusoidal fringe obtained by Fourier transform contour technique method in step two is marked as φ=[ϕ₁, ϕ₂, L, ϕ_(n)]^(T). Because the resolution of the projector along the direction of the sinusoidal fringe intensity is limited, so the possible fringe order combinations are also limited, the fringe order combinations are listed one by one (Petković T, Pribanić T, Ðonlić M. “Temporal phase unwrapping using orthographic projection”. Optics & Lasers in Engineering, 2017, 90: 34-47.), and each set of fringe order sub-vectors is recorded as k, which contains the corresponding fringe order of each wrapped phase [k₁, k₂, L, k_(n)]^(T), for each fringe order vector k_(i), the corresponding absolute phase Φ, is calculated by the following formula:

Φ_(i)=φ+2πk _(i)   (8)

where Φ_(i) is the absolute phase vector, q is the wrapped phase vector, k_(i) is the fringe-level sub-vector, and then the projection point vector of the absolute phase is calculated by equations (9) and (10):

$\begin{matrix} {t = {{\left( {\lambda^{- 1}}^{2} \right)^{1}\left( \lambda^{- 1} \right)^{T}\Phi_{i}} = {\left( {\sum_{j = 1}^{n}\left( \frac{1}{\lambda_{j}^{2}} \right)} \right)^{- 1}{\sum_{j = 1}^{n}\frac{\Phi_{j}}{\lambda_{i}}}}}} & (9) \\ {P_{i} = {t\; \lambda_{i}^{- 1}}} & (10) \end{matrix}$

where λ_(i) is the wavelength vector, Φ_(i) is the absolute phase vector, n is the number of projected sinusoidal fringes, P_(i) is the projection point vector, and finally the distance d_(i) ² between the two is obtained by the formula

d _(i) ² =∥P _(i)−Φ_(i)∥²=(P _(i)−Φ_(i))^(T)(P _(i)−Φ_(i))   (11)

selecting the fringe-order sub-vector corresponding to the minimum distance d_(min) ² as the optimal solution, and then the absolute phase Φ corresponding to the optimal solution is obtained as the initial absolute phase.

The measurement range of the measurement subsystem is definitely limited, and the range of fringe order combination is further narrowed down, that is, firstly estimating the depth range of the measured scene [z_(min) ^(w), z_(max) ^(w)], z_(min) ^(w) is the minimum value of the depth of the measurement range in the world coordinate system, z_(max) ^(w) is the maximum value of the depth of the measurement range in the world coordinate system, and the range of the phase distribution is obtained according to the calibration parameters and the method (real-time structured light illumination three-dimensional topography measurement method)mentioned by Liu K. in (Liu K. “Real-time 3-d reconstruction by means of structured light illumination” 2010.), i.e., [Φ_(min), Φ_(max)], Φ_(min) is the minimum value of the absolute phase, and Φ_(max) is the maximum value of the absolute phase, so that the range of fringe order is obtained by the following formula:

$\begin{matrix} {{k_{\min}\left( {x^{c},y^{c}} \right)} = {{floor}\left\lbrack \frac{\Phi_{\min}\left( {x^{c},y^{c}} \right)}{2\pi} \right\rbrack}} & (12) \\ {{k_{\max}\left( {x^{c},y^{c}} \right)} = {{ceil}\left\lbrack \frac{\Phi_{\max}\left( {x^{c},y^{c}} \right)}{2\pi} \right\rbrack}} & (13) \end{matrix}$

where k_(min) represents the minimum value of fringe order, k_(max) represents the maximum value of fringe order, (x^(c), y^(c)) represents the pixel coordinates of the camera, floor represents the round-down operation, and Φ_(min) represents the phase minimum, ceil represents the rounding up operation, and Φ_(max) represents the phase maximum. Reducing the range of fringe order can eliminate a part of wrong fringe order combinations to reduce the error points and improve the measurement precision. Step five, the initial absolute phase is corrected by using reliability guided compensation (RGC) of fringe order error method. The specific process is as follows: because images captured by a camera may have lower quality (such as small fringe contrast) and the influence of the fast motion of a measured object between each frame cannot be ignored and the absolute phase obtained in step four may have the problem of the fringe order error, so reliability guided compensation (RGC) of fringe order error method can further correct the absolute phase in spacial domain, which can correct these errors and improve the measurement precision. The two main problems in the reliability guided compensation (RGC) of fringe order error method are which index is selected as the reliability parameter, that is, how to evaluate whether the absolute phase corresponding to a pixel is correct and how to design a correction path. The minimum projection distance corresponding to each pixel d_(min) ² in step four is used as the basis for evaluating the reliability of an absolute phase (the larger the d_(min) ² is, the lower the absolute phase reliability is), the reliability at the pixel boundary is defined by the sum of the reliability of two adjacent pixels; by comparing the reliability value at the pixel boundary, the path to be processed is determined, that is, the correction is performed from the pixel with a large reliability value, and the reliability value at the intersection of all pixels is stored in a queue, and is sorted according to the amount of reliability value, and the greater the credibility value is, the first it is processed, thus resulting in a corrected absolute phase.

The specific steps of the above processing are:

(1) calculating the reliability value of each pixel boundary, that is, adding the minimum projection distance d_(min) ² obtained by the previous step corresponding to the two pixels connected at the boundary as the reliability value at the pixel boundary;

(2) The adjacent pixels are sequentially determined. If the absolute value of the phase value difference corresponding to the adjacent pixels is less than π, the two pixels are grouped into one group, and all the pixels are grouped according to this method;

(3) Absolute phases are sequentially corrected according to the order of credibility values at the pixel boundaries. The higher the credibility is, the first it is processed; if two connected pixels belong to the same group, no processing is performed; if two connected pixels belong to different groups and the number of pixels of the group with a small number of pixels is less than a threshold T_(h) (the value of T_(h) is determined according to a specific case, the number of pixels smaller than T_(h) is considered to be a wrong point, and the number of pixels larger than T_(h) is a separate object), all phase values in the smaller group are corrected according to the group with a larger number of pixels and the two groups are combined, that is, the phase values corresponding to the pixels belonging to the groups having a larger number of pixels and the smaller number of pixels are respectively Φ_(L) and Φ_(S), and the value of

${Round}\mspace{11mu} \left( \frac{\Phi_{L} - \Phi_{S}}{2\pi} \right)$

multiplied by 2π is added to the phase value corresponding to all the pixels in the group with a smaller number of pixels, and the two groups are combined; Round means rounding off;

(4) Repeat step (3) until all pixel boundaries in the queue have been processed.

Through the above steps, the process of correcting the obtained absolute phase by using the reliability guided compensation (RGC) of fringe order error method is completed, thus the absolute phase error can be corrected, and the measurement precision is further improved.

Step six, the three-dimensional reconstruction is performed by using the calibration parameters and the corrected absolute phase, thereby accomplishing the three-dimensional topography measurement, and the specific process is as follows: combining the following formula with the calibration parameters obtained in step one (i.e., the internal parameters and the external parameters of the camera and the projector) and the corrected absolute phase Φ obtained in step five, the final three-dimensional world coordinates are obtained to accomplish the reconstruction:

$\begin{matrix} {{{x_{p} = \frac{\Phi W}{2\pi \; N_{L}}}{Z_{p} = {M_{Z} + \frac{N_{Z}}{{C_{Z}x_{p}} + 1}}}}{X_{p} = {{E_{X}Z_{p}} + F_{X}}}{Y_{p} = {{E_{Y}Z_{p}} + F_{Y}}}} & (14) \end{matrix}$

where E_(X),F_(X), E_(Y), F_(Y), M_(Z), N_(Z), C_(Z) are intermediate variables, which are obtained by the method in (K. Liu, Y. Wang, et al “Dual-frequency pattern scheme for high-speed 3-D shape measurement.” Optics express.18(5), 5229-5244 (2010). and Φ is the absolute phase, W is the resolution of the projector along the direction of fringe intensity variation, N_(L) is the corresponding number of fringes, x_(p) is the projector coordinates, and X_(p), Y_(p), Z_(p) are three-dimensional spacial coordinates of the measured object in a world coordinate system, thus obtaining the three-dimensional data of the measured scene at the current moment, and then the 2D image sequence is taken as a sliding window according to the above steps to repeatedly process the captured two-dimensional pattern sequences to obtain the three-dimensional topography reconstruction results of the super-rapid motion scene for the whole measurement period.

In combination with FIG. 1 and FIG. 5, a super-rapid three-dimensional topography measurement method its and system based on an improved Fourier transform contour technique comprising: a measuring subsystem, a Fourier transform contour technique subsystem, a calibration unit, a projection and acquisition image unit, and a three-dimensional reconstruction unit;

the measuring subsystem consists of a projector, a camera and a computer; the Fourier transform contour technique subsystem consists of a background normalized Fourier transform contour technique module, a temporal phase unwrapping with projection distance minimization (PDM) module and a reliability guided compensation (RGC) of fringe order error module;

the calibration unit calibrates the measurement subsystem to obtain calibration parameters;

in the projection and acquisition image unit, the projector projects 2n (n≥2) patterns cyclically onto the measured scene, wherein n patterns are binary high-frequency sinusoidal fringes with different wavelengths, n patterns are all-white images with pixel value of 1, all-white images are projected between every two binary high-frequency sinusoidal fringes, and images are captured synchronously by a camera;

the background normalized Fourier transform contour technique module processes the captured images to get wrapped phases, and then a initial absolute phase is obtained through the temporal phase unwrapping with projection distance minimization (PDM) module and then using reliability guided compensation (RGC) of fringe order error module to correct the initial absolute phase;

reconstructing a three-dimensional topography of the measured scene with the corrected absolute phase and the calibration parameters through the three-dimensional reconstruction unit to obtain three-dimensional spacial coordinates of the measured scene in a world coordinate system, thereby accomplishing three-dimensional topography measurement of an object.

The specific implementation processes of projecting and acquiring the image unit, the three-dimensional reconstruction unit, the background normalized Fourier transform contour technique module, the temporal phase unwrapping with projection distance minimization (PDM) module and the reliability guided compensation (RGC) of fringe order error module are as shown in the above steps.

The measurement precision and the measurement speed of the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique are verified by experiments. In the experiment, a three-dimensional topography measurement system is built by using a projector with a binary pattern projection speed, a camera with an image acquisition speed of 20000 Hz, and a computer. The resolution of the projector is 1024×768. Cyclically projecting six binary images onto the measured scene, three of which are binary high-frequency sinusoidal fringes with wavelengths {λ₁, λ₂, λ₃}={14, 16, 18} (in pixels), three of which are all-white images with the values of 1, the all-white images are projected between binary high-frequency fringes, and images are synchronously acquired using a camera. The experimentally constructed system realized reconstruction rate at 10000 frames per second with absolute three-dimensional topography. Under the measurement range of 400 mm×275 mm×400 mm, the depth precision is 80 μm, and the time domain error is less than 75 μm. The experiments measure a complex set of static scenes, including a plaster statue and a hand and two sets of high-speed motion scenes, respectively, the toy gun popping up and hitting a plastic sheet and bouncing back and the darts flying and hitting the balloon and causing the balloon to explode. The drawings illustrate the experimental results in detail.

FIG. 2 is the experimental result of three-dimensional topography measurement of a static scene containing a plaster image and a hand using the super-rapid three-dimensional topography measurement method based on an improved Fourier transform contour technique. (a1)-(a3) are the images acquired by the camera when the binary high-frequency sinusoidal fringes are projected onto the measured scene; (a4)are the images acquired by the camera when all-white images are projected onto the measured scene; (b1)-(b3) are the wrapped phase maps obtained by the background normalized Fourier transform contour; (b4) is the minimum projection distance (d_(min) ²) corresponding to each pixel point obtained by the temporal phase unwrapping with projection distance minimization (PDM) method; (c1)-(c3) are the initial absolute phase maps obtained by the temporal phase unwrapping with projection distance minimization (PDM) method; (c4) is the three-dimensional topography measurement result reconstructed according to the phase corresponding to (c2); (d1)-(d3) is the absolute phase map after the depth constraint being added to the temporal phase unwrapping with projection distance minimization (PDM) method and limited fringe-level search range. It can be seen that error points are significantly reduced and the measurement precision is improved; (d4) is the reconstructed 3D topography measurement results based on the phase corresponding to (d2); (e1)-(e3) are the absolute phase maps corrected by the reliability guided compensation (RGC) of fringe order error method for the initial absolute phase, and it can be seen that the error points are further reduced, and the measurement precision is improved again; (e4) is the reconstructed 3D topography measurement result based on the phase corresponding to (e2). It can be seen that the three-dimensional topographical measurements obtained after these steps have almost no errors. It fully demonstrates that the super-rapid three-dimensional topography measurement method based on the improved Fourier transform contour technique has high measurement precision.

FIG. 3 is the result of three-dimensional topography measurement using the super-rapid three-dimensional topography measurement method based on the improved Fourier transform contour technique on a scene in which a toy gun pops up and hits a plastic plate and bounces. (a) are the images acquired by cameras corresponding to different time points; (b) are the three-dimensional topography measurement results corresponding to the two-dimensional images in (a); (c) are the three-dimensional topography measurement results when the bullets are just out of the muzzle (corresponding to the block area in Figure (b)) and the three-dimensional topography measurements corresponding to the bullets at three times (7.5 ms, 12.6 ms, 17.7 ms). The illustration in Figure (c) shows the contour technique of the bullet corresponding to the 17.7 ms time from different sides; (d) is the 3D topography measurement result corresponding to the last moment (135 ms), the curve in the figure shows the movement trajectory of the bullet in the period of 135 ms period, the illustration in Figure (d) is a curve graphics of bullet velocity versus time.

The experimental results fully demonstrate that the super-rapid three-dimensional topography measurement method based on the improved Fourier transform contour technique can accurately retrieve the three-dimensional topography of the whole process of rebounding the toy gun and hitting a plastic plate, which proves high speed and precision of the three-dimensional topography measurement method.

FIG. 4 is a result of three-dimensional topography measurement of a scene in which a darts flies and hits a balloon to cause a balloon explosion using the super-rapid three-dimensional topography measurement method based on the improved Fourier transform contour technique. (a) are the images acquired by cameras corresponding to different time points; (b) are the three-dimensional topography measurement results corresponding to the two-dimensional images in (a); (c) and (d) are respectively follow-up of (a) and (b); (e) is the three-dimensional topographic reconstruction contour technique corresponding to the dotted line on the balloon identified in Figure (a) corresponding to 10.7 ms, 11.4 ms, 12.1 ms, 12.8 ms, and 13.7 ms.

The experimental results fully demonstrate that the super-rapid three-dimensional topography measurement method based on the improved Fourier transform contour technique can accurately retrieve the three-dimensional topography of the whole process of the balloon explosion caused by the dart flying to hit the balloon, which proves the three-dimensional shape measurement method has high speed and precision. 

1. A super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized by firstly calibrating a measurement system to obtain calibration parameters, the measurement system being composed of a projector, a camera and a computer, and then cyclically projecting 2n (n≥2)patterns into a measured scene using a projector, wherein n patterns are binary sinusoidal fringes with different high frequency fringe, and the other n patterns are all-white images with the values of 1, and projecting the all-white images between every two binary high-frequency sinusoidal fringes and synchronously acquiring images using a camera; then using the background normalized Fourier transform contour method to obtain the wrapped phase, using temporal phase unwrapping with projection distance minimization (PDM) method to obtain initial absolute phases, using a reliability guided compensation (RGC) of fringe order error method to correct the initial absolute phase, and finally reconstructing a three-dimensional topography of the measured scene with the corrected absolute phases and the calibration parameters to obtain 3D spatial coordinates of the measured scene in a world coordinate system, thereby accomplishing three-dimensional topography measurement of an object.
 2. According to claim 1, the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized in that the specific process of projection and acquisition of images is as follows: n high-frequency sinusoidal fringe emitted by the projector must be different in wavelength and the wavelength is marked as {λ₁, λ₂, . . . , λ_(n)}; two conditions must be met when designing the wavelength: {circle around (1)} The wavelength of the sinusoidal fringe is small enough to ensure the phase can be successfully retrieved by the traditional Fourier transform contour technique; {circle around (2)} The least common multiple of the wavelength is greater than or equal to the resolution of the projector along the sinusoidal intensity value, denoted as W, that is, the following formula is satisfied: LCM(λ₁, λ₂ , L, λ _(n))≥W   (1) where LCM represents the least common multiple operation and the generated high-frequency sinusoidal fringes are represented by the following formula in the projector space: I ^(p)(x ^(p) , y ^(p))=a ^(p) +a ^(p) cos(2πf ₀ ^(p) x ^(p))   (2) where the superscript p represents the projector space, and I^(p) represents the intensity of fringes (x^(p), y^(p)) is the pixel coordinates of the projector, a^(p) is the average intensity of the sinusoidal fringes, b^(p) is the amplitude of the sinusoidal fringes and f₀ ^(p) is the frequency of the sinusoidal fringes; the halftone technique is then used to convert the high-frequency sinusoidal fringes into binary high-frequency sinusoidal fringes, so that the projection speed of the projector can reach the maximum of the inherent projection speed of the projector, ensuring that the hardware does not affect the measurement speed; as the fringe pattern is a binary pattern, both a^(p) and b^(p) in equation (2) are ½, and equation (2) is written as: I ₁ ^(p)(x ^(p) , y ^(p))=1/2+1/2 cos(2πf ₀ ^(p) x ^(p))   (3) where I₁ ^(p) represents the intensity of the first high-frequency sinusoidal fringe pattern, the all-white images projected between every two binary high-frequency sinusoidal fringes mean that the values of all the pixels on the projected image are “1”, that is, all micro-mirrors on the digital micro-mirror device (DMD) as a key component of digital light processing (DLP) projection system, are the “on” state and are represented by the following formula: I ₂ ^(p)(x ^(p) , y ^(p))=1   (4) where I₂ ^(p) represents the intensity of the all-white images, (x^(p), y^(p)) represents the pixel coordinates of the projector, and the expression of the remaining high-frequency sinusoidal fringe is the same as formula (3), except that the frequency f₀ ^(p) is different according to the different wavelength; 2n images are cyclically projected into a measured scene using a projector, and the camera synchronously acquires the image using the trigger signal of the projector.
 3. According to claim 1, the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized in that the wrapped phase is obtained by using a background normalized Fourier transform contour technique method, and the specific process is as follows: after the acquisition of images by a camera, every two images are sequentially processed, that is, a high-frequency sinusoidal fringe and a corresponding all-white image; the high-frequency sinusoidal fringe image and the all-white image captured by a camera are respectively expressed by the following formulas: I ₁(x ^(c) , y ^(c))=1/2α(x ^(c) , y ^(c))+1/2α(x ^(c) , y ^(c))cos[2πf ₀ x ^(c)+ϕ(x ^(c) , y ^(c))]  (5) I ₂(x ^(c) , y ^(c))=α(x ^(c) , y ^(c))   (6) where the superscript c represents a camera space, I₁ is an image captured by a camera after the high-frequency sinusoidal fringe pattern is projected onto the measured scene, I₂ is an image captured by the camera after the all-white image is projected onto the measured scene, (x^(c), y^(c)) is pixel coordinates of the camera, α(x^(c), y^(c)) is the reflectivity of the measured object, f₀ is the sinusoidal fringe frequency, ϕ(x^(c), y^(c)) is the phase containing the depth information of the object, ½α(x^(c), y^(c)) is the zero-frequency part after performing Fourier transform; by using I₁ and I₂, the influence of the zero-frequency part and the surface reflectivity α(x^(c), y^(c)) of the object to be measured can be removed before performing the Fourier transform, see equation (7): $\begin{matrix} {{I_{d}\left( {x^{c},y^{c}} \right)} = {\frac{{2I_{1}} - l_{2}}{I_{2} + \gamma} = {\cos \left\lbrack {{2\pi f_{0}x^{c}} + {\varphi \left( {x^{c},y^{c}} \right)}} \right\rbrack}}} & (7) \end{matrix}$ where γ is a constant; then Fourier transform is performed on the I_(d) after background normalization, using a filter to extract the valid information, and then the wrapped phase is obtained by performing the inverse Fourier transform; through this procedure, the wrapped phases corresponding to each high-frequency sinusoidal fringe acquired by the camera are obtained and contain the depth information of the scene corresponding to each moment when the camera captures the high-frequency sinusoidal fringe pattern.
 4. According to claim 1, the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized in that the initial absolute phase is obtained by using a temporal phase unwrapping with projection distance minimization (PDM) method, and the specific process is as follows: using the wrapped phases corresponding to a set of high-frequency sinusoidal fringes to unwrap each of wrapped phases. The high-frequency sinusoidal fringes projected by a projector are different in wavelength, and are recorded as a wavelength vector λ=[λ₁, λ₂, L, λ_(n)]^(T); the wrapped phase vector corresponding to each high-frequency sinusoidal fringe obtained by Fourier transform contour technique method is marked as φ=[ϕ₁, ϕ₂, L, ϕ_(n)]^(T); the fringe order combinations are listed one by one, and each set of fringe-level sub-vectors is recorded as k_(i), which contains the corresponding fringe order of each wrapped phase [k₁, k₂, L, k_(n)]^(T), for each fringe order vector k_(i), the corresponding absolute phase Φ_(i) is calculated by the following formula: Φ_(i)=φ+2πk _(i)   (8) where Φ_(i) is the absolute phase vector, φ is the wrapped phase vector, k_(i) is the fringe order sub-vector, and then the projection point vector of the absolute phase is calculated by equations (9) and (10): $\begin{matrix} {t = {{\left( {\lambda^{- 1}}^{2} \right)^{1}\left( \lambda^{- 1} \right)^{T}\Phi_{i}} = {\left( {\sum_{j = 1}^{n}\left( \frac{1}{\lambda_{j}^{2}} \right)} \right)^{- 1}{\sum_{j = 1}^{n}\frac{\Phi_{j}}{\lambda_{i}}}}}} & (9) \\ {P_{i} = {t\; \lambda_{i}^{- 1}}} & (10) \end{matrix}$ where λ_(i) is the wavelength vector, Φ_(i) is the absolute phase vector, n is the number of projected sinusoidal fringes, P_(i) is the projection point vector, and finally the distance d_(i) ² between Φ_(i) and P_(i) is obtained by the formula d _(i) ² =∥P _(i)−Φ_(i)∥²=(P _(i)−Φ_(i))^(T)(P _(i)−Φ_(i))   (11) selecting the fringe-order sub-vector corresponding to the minimum distance d_(min) ² as the optimal solution, and the absolute phase Φ corresponding to the optimal solution is obtained as the initial absolute phase.
 5. According to claim 4, the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized in that the range of enumerated fringe-level sub-combinations is further reduced by depth constraint, that is, firstly estimating the depth range of the measured scene [z_(min) ^(w), z_(max) ^(w)], z_(min) ^(w) is the minimum value of the depth of the measurement range in the world coordinate system, z_(max) ^(w) is the maximum value of the depth of the measurement range in the world coordinate system, and the range of the phase distribution is obtained according to the calibration parameters and the depth constraint method, i.e., [Φ_(min), Φ_(max)], Φ_(min) is the minimum value of the absolute phase and Φ_(max) is the maximum value of the absolute phase, thus the range of fringe order is obtained by the following formula: $\begin{matrix} {{k_{\min}\left( {x^{c},y^{c}} \right)} = {{floor}\left\lbrack \frac{\Phi_{\min}\left( {x^{c},y^{c}} \right)}{2\pi} \right\rbrack}} & (12) \\ {{k_{\max}\left( {x^{c},y^{c}} \right)} = {{ceil}\left\lbrack \frac{\Phi_{\max}\left( {x^{c},y^{c}} \right)}{2\pi} \right\rbrack}} & (13) \end{matrix}$ where k_(min) represents the minimum value of fringe order, k_(max) represents the maximum value of fringe order, (x^(c), y^(c)) represents the pixel coordinates of the camera, floor represents the round-down operation, and Φ_(min) represents minimum value of the phase, ceil represents the rounding up operation, and Φ_(max) represents maximum value of the phase.
 6. According to claim 1, the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized in that the initial absolute phase is corrected by using a reliability guided compensation (RGC) of fringe order error method, and the specific process is as follows: the minimum projection distance corresponding to each pixel d_(min) ² is used as the basis for evaluating the reliability of the absolute phase; the reliability at the pixel boundary is defined by the sum of the reliability of the adjacent two pixels; by comparing the reliability value at the pixel boundary, the path to be processed is determined, that is, the correction is performed from the pixel with a large reliability value, and the reliability value at the intersection of all pixels is stored in a queue, and is sorted according to the amount of credibility value, and the greater the credibility value is, the first it is processed, thus resulting in a corrected absolute phase.
 7. According to claim 6, the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized in that the specific steps of reliability guided compensation (RGC) of fringe order error method are: (1) the credibility value of each pixel boundary is calculated, that is, the minimum projection distance d_(min) ² obtained by temporal phase unwrapping with projection distance minimization (PDM) method corresponding to the two pixels connected at the boundary are added as the credibility value at the pixel boundary; (2) The adjacent pixels are sequentially determined. If the absolute difference of the phase value corresponding to the adjacent pixels is less than π, the two pixels are grouped into one group, and all the pixels are grouped according to this method; (3) Absolute phases are sequentially corrected according to the order of credibility values at the pixel boundaries; the higher the credibility, the first processed; if two connected pixels belong to the same group, no processing is performed; if two connected pixels belong to different groups and the number of pixels of the group with a small number of pixels is less than a threshold T_(h), all phase values in the smaller group are corrected according to the group with a larger number of pixels and the two groups are combined, that is, the phase values corresponding to the pixels belonging to the groups having a larger number of pixels and the smaller number of pixels are respectively Φ_(L) and Φ_(S), and the value of ${Round}\mspace{11mu} \left( \frac{\Phi_{L} - \Phi_{S}}{2\pi} \right)$ multiplied by 2π is added to the phase value Φ_(S) corresponding to all the pixels in the group having a smaller number of pixels, and the two groups are combined; Round means rounding off; (4) Repeat step (3) until all pixel boundaries in the queue have been processed.
 8. According to claim 1, the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized in that the three-dimensional reconstruction is performed by using the calibration parameters and the corrected absolute phase, thereby accomplishing three-dimensional topography measurement, and the specific process is as follows: combining the following formula with the calibration parameters and the corrected absolute phase (I), the final three-dimensional world coordinates are obtained so as to complete the reconstruction: $\begin{matrix} {{{x_{p} = \frac{\Phi W}{2\pi \; N_{L}}}{Z_{p} = {M_{Z} + \frac{N_{Z}}{{C_{Z}x_{p}} + 1}}}}{X_{p} = {{E_{X}Z_{p}} + F_{X}}}{Y_{p} = {{E_{Y}Z_{p}} + F_{Y}}}} & (14) \end{matrix}$ where E_(X), F_(X), E_(Y), F_(Y), M_(Z), N_(Z), C_(Z) are intermediate variables, and Φ is the absolute phase, W is the resolution of the projector along the direction of fringe intensity variation, N_(L) is the corresponding number of fringes, x_(p) is the projector coordinates, and X_(p), Y_(p), Z_(p) are three-dimensional spatial coordinates of the measured object in a world coordinate system, the three-dimensional data of the measured scene at the current moment is obtained, and then the collected two-dimensional pattern sequences are repeatedly processed so as to obtain the three-dimensional topography reconstruction result of the super-rapid motion scene for the whole measurement period.
 9. A super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized by comprising a measuring subsystem, a Fourier transform contour technique subsystem, a calibration unit, a projection and acquisition image unit, and a three-dimensional reconstruction unit; the measuring subsystem consists of a projector, a camera and a computer; the Fourier transform contour technique subsystem consists of a background normalized Fourier transform contour technique module, temporal phase unwrapping with projection distance minimization and a a reliability guided compensation module; the calibration unit calibrates the measurement subsystem so as to obtain calibration parameters; in projection and acquisition image unit, the projector projects 2n patterns cyclically to the measured scene, n≥2, wherein n patterns are binary high-frequency sinusoidal fringes with different wavelengths, n are with pixel value of 1, all-white images are projected between every two binary high-frequency sinusoidal fringes, and images are collected synchronously by a camera; the background normalized Fourier transform contour technique module processes the collected images so as to get wrapped phases, and then a preliminary absolute phase is obtained by the temporal phase unwrapping with projection distance minimization (PDM) module and then using reliability guided compensation (RGC) of fringe order error module to correct the initial absolute phase; reconstructing a three-dimensional topography of the measured scene with the corrected absolute phase and the calibration parameters through the three-dimensional reconstruction unit to obtain three-dimensional spacial coordinates of the measured scene in a world coordinate system, thereby accomplishing three-dimensional topography measurement of an object.
 10. According to claim 9, the super-rapid three-dimensional topography measurement method and system based on an improved Fourier transform contour technique is characterized by the background normalized Fourier transform contour technique module, after acquiring images collected by a camera, every two images are sequentially processed, that is, a high-frequency sinusoidal fringe and a corresponding all-white image; the high-frequency sinusoidal fringe image and the all-white image captured by a camera are respectively expressed by the following formulas: I ₁(x ^(c) , y ^(c))=1/2α(x ^(c) , y ^(c))+1/2α(x ^(c) , y ^(c))cos[2πf ₀ x ^(c)+ϕ(x ^(c) , y ^(c))]  (5) I ₂(x ^(c) , y ^(c))=α(x ^(c) , y ^(c))   (6) where the superscript c represents a camera space, I₁ is an image captured by a camera after the high-frequency sinusoidal fringe pattern is projected onto the measured scene, I₂ is an image captured by the camera after the all-white image is projected onto the measured scene, (x^(c), y^(c)) is pixel coordinates of the camera, α(x^(c), y^(c)) is the reflectivity of the measured object, f₀ is the sinusoidal fringe frequency, ϕ(x^(c), y^(c)) is the phase containing the depth information of the object, ½α(x^(c), y^(c)) is the zero-frequency part after performing Fourier transform; by using I₁ and I₂, the influence of the zero-frequency part and the surface reflectivity α(x^(c), y^(c)) of the object to be measured can be removed before performing the Fourier transform, see equation (7): $\begin{matrix} {{I_{d}\left( {x^{c},y^{c}} \right)} = {\frac{{2I_{1}} - l_{2}}{I_{2} + \gamma} = {\cos \left\lbrack {{2\pi f_{0}x^{c}} + {\varphi \left( {x^{c},y^{c}} \right)}} \right\rbrack}}} & (7) \end{matrix}$ where γ is a constant; then Fourier transform is carried out on the I_(d) after background normalization, and a filter is used to extract the valid information, then using the inverse Fourier transform to obtain the wrapped phase; through this procedure, the wrapped phase corresponding to each high-frequency sinusoidal fringe acquired by the camera is obtained and contains the depth information of the scene corresponding to each moment when the camera captures the high-frequency sinusoidal fringe pattern; in the temporal phase unwrapping with projection distance minimization (PDM) module, using the wrapped phases corresponding to a set of sinusoidal fringes to unwrap each of wrapped phases; the high-frequency sinusoidal fringes projected by a projector are different in wavelength, and are recorded as a wavelength vector λ=[λ₁, λ₂, L, λ_(n)]^(T), the wrapped phase vector corresponding to each high-frequency sinusoidal fringe obtained by Fourier transform contour technique is marked as φ=[ϕ₁, ϕ₂, L, ϕ_(n)]^(T), the fringe order sub-combinations are listed one by one, and each set of fringe order sub-vectors is recorded as k_(i) which contains the corresponding fringe order of each wrapped phase [k₁, k₂, L, k_(n)]^(T), for each fringe order vector k_(i), the corresponding absolute phase Φ_(i) is calculated by the following formula: Φ_(i)=φ+2πk _(i)   (8) where Φ_(i) is the absolute phase vector, φ is the wrapped phase vector, k_(i) is the fringe order sub-vector, and then the projection point vector of the absolute phase is calculated by equations (9) and (10): $\begin{matrix} {t = {{\left( {\lambda^{- 1}}^{2} \right)^{1}\left( \lambda^{- 1} \right)^{T}\Phi_{i}} = {\left( {\sum_{j = 1}^{n}\left( \frac{1}{\lambda_{j}^{2}} \right)} \right)^{- 1}{\sum_{j = 1}^{n}\frac{\Phi_{j}}{\lambda_{i}}}}}} & (9) \\ {P_{i} = {t\; \lambda_{i}^{- 1}}} & (10) \end{matrix}$ where λ_(i) is the wavelength vector, Φ_(i) is the absolute phase vector, n is the number of projected sinusoidal fringes, P_(i) is the projection point vector, and finally the distance d_(i) ² between Φ_(i) and P_(i) is obtained by the formula d _(i) ² =∥P _(i)−Φ_(i)∥²=(P _(i)−Φ_(i))^(T)(P _(i)−Φ_(i))   (11) selecting the fringe-order sub-vector corresponding to the minimum distance d_(min) ² as the optimal solution, and then the absolute phase Φ corresponding to the optimal solution is obtained as the initial absolute phase; In the reliability guided compensation (RGC) of fringe order error module: the minimum projection distance d_(min) ² corresponding to each pixel is used as the basis for evaluating the reliability of absolute phase. The reliability at the pixel boundary is defined by the sum of the credibility of the adjacent two pixels; by comparing the reliability value at the pixel boundary, the path to be processed is determined, that is, the correction is performed from the pixel with a large reliability value; the reliability value at the intersection of all pixels is stored in a queue and sorted according to the amount of credibility value, the greater the credibility value is, the first it is processed, thus resulting in a corrected absolute phase. 